Measures of Variation - Notes & Practice

Measures of Variation - Notes & Practice

Measures of Variation are used to describe the distribution, or spread of a set of data. They use a single number to describe how the values of a data set vary. A quartile is one measure of variation.

Quartiles are values that divide a data set into four equal parts.

The first quartile is the median of the data values less than the median. The third quartile is the median of the data values greater than the median. The interquartile range (IQR) is the distance between the first and third

quartiles. If the interquartile range is low, the middle data are grouped closely together.

Range: The range is the difference between the greatest and the least values in the data set.

Example:

Median = 3.5

1

1

One?fourth of the data is below the

4

4

first quartile and one-fourth of the

data is above the third quartile. One

half of the data lie between the first

and third quartile.

Think: Which measure of center would be most affected by an outlier? Justify your answer.

Outliers: An outlier is a data value that is either much greater than or much less than the median. If a data value is more than 1.5 times the value of the interquartile range beyond the quartiles, it is considered an outlier.

Practice:

1. Determine the measures of variation for the given data set. Are there any outliers in the data set? Justify your answer.

64, 61, 67, 59, 60, 58, 57, 78, 56, 62

2. The temperatures for the first half of the year are given for Antelope, Montana and

Augusta, Maine. Compare and contrast the measures of variation for the two cities.

Month January February March

April May June

Montana 21 30 42 58 70 79

Maine 28 32 41 53 66 75

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